Geometric Sequence Calculator

Calculate the sum of first n terms and the nth term of geometric sequence

First term (a₁):

Common ratio (r):

Number of terms (n):

Result

Calculation Steps

About the Geometric Sequence Calculator

A geometric sequence is a sequence in which the ratio between any two adjacent terms is the same; this ratio is called the common ratio. Geometric sequences are widely used in math, physics, and finance, such as compound interest, radioactive decay, and population growth models. Enter the first term (a1), the common ratio (r), and the term count (n) as needed, and the results show the sum of the first n terms and the value of the nth term.

Geometric Sequence Formulas

General term formula: an = a1 × r^(n-1)
Sum of the first n terms: when r ≠ 1, Sn = a1(1 - rⁿ)/(1 - r); when r = 1, Sn = n × a1
Sum of an infinite series: when |r| < 1, S = a1/(1 - r)